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Lazy Queue Layouts of Posets

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Graph Drawing and Network Visualization (GD 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12590))

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Abstract

We investigate the queue number of posets in terms of their width, that is, the maximum number of pairwise incomparable elements. A long-standing conjecture of Heath and Pemmaraju asserts that every poset of width w has queue number at most w. The conjecture has been confirmed for posets of width \(w=2\) via so-called lazy linear extension.

We extend and thoroughly analyze lazy linear extensions for posets of width \(w > 2\). Our analysis implies an upper bound of \((w-1)^2 +1\) on the queue number of width-w posets, which is tight for the strategy and yields an improvement over the previously best-known bound. Further, we provide an example of a poset that requires at least \(w+1\) queues in every linear extension, thereby disproving the conjecture for posets of width \(w > 2\).

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Notes

  1. 1.

    Knauer et al. [16] also claim to reduce the queue number of posets of width w from \(w^2\) to \(w^2 - 2\lfloor w/2 \rfloor \). However, as we discuss in [2], their argument is incomplete.

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Authors and Affiliations

  1. Amazon Inc., Tempe, AZ, USA

    Jawaherul Md. Alam

  2. Institut für Informatik, Universität Tübingen, Tübingen, Germany

    Michael A. Bekos & Michael Kaufmann

  3. Theoretical Computer Science, Osnabrück University, Osnabrück, Germany

    Martin Gronemann

  4. Facebook, Inc., Menlo Park, CA, USA

    Sergey Pupyrev

Authors
  1. Jawaherul Md. Alam
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  2. Michael A. Bekos
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  3. Martin Gronemann
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  4. Michael Kaufmann
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  5. Sergey Pupyrev
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Corresponding author

Correspondence to Michael A. Bekos .

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Editors and Affiliations

  1. LaBRI, University of Bordeaux, Talence, France

    David Auber

  2. Charles University, Prague, Czech Republic

    Pavel Valtr

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Alam, J.M., Bekos, M.A., Gronemann, M., Kaufmann, M., Pupyrev, S. (2020). Lazy Queue Layouts of Posets. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_5

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  • DOI: https://doi.org/10.1007/978-3-030-68766-3_5

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